A post SQUID ac amplifier aimed for multiplexed detector readouts

Transcription

1 A post SQUID ac amplifier aimed for multiplexed detector readouts Mikko Kivirata, Atti Virtae, Heikki Seppä, Jari Pettilä, Juha Hassel ad Pau Helistö Abstract We have built a room temperature amplifier based o Si JFETs iteded for ac coupled SQUID readouts, such as frequecy domai multiplexed trasitio edge sesor systems. The amplifier operates at 5 MHz ceter frequecy where it has the measured oise temperature of 7 K for a 6 ohm load, which icludes the oise from the active termiatio ad the room temperature trasformer. Whe drive from a SQUID with a o chip matchig trasformer flux oise of.45 µ Φ Hz / has bee obtaied. Additioally, we cosider the potetial of the recetly itroduced SiGe bipolar trasistors for the same applicatio. The dyamic rage cosideratios i SQUID multiplexers, which require the use of a amplifier with a low oise temperature, are briefly discussed. T I. INTRODUTION HE achieved oise level i dc SQUID systems is ofte domiated by the first room temperature amplifier stage. A simple calculatio based o autoomous SQUID equatios reveals that the oise temperature at the output of a dc SQUID havig o excess oise is theoretically.4 times the cryogeic bath temperature T cr, assumig β c = β L = but regardless of other desig parameters. Such oise temperature is difficult to reach by semicoductor devices eve whe T cr = 4. K ad eve more difficult if the SQUID is operated at sub kelvi temperatures. Reductio of the system oise is particularly importat whe oe eeds a large dyamic rage, limited by the oise floor at the low ed ad by the maximum tolerated o liearity at the high ed. Such a eed is particularly pressig i frequecy domai multiplexed (FDM) readouts of cryogeic detectors [], but similar eed appears also i time domai multiplexig (TDM) []. A. Dyamic rage budget II. NEED FOR DYNAMI RANGE A serious desig costrait i SQUID multiplexers is the dyamic rage requiremet i the sigal path, simultaeously with a sufficiet badwidth [3]. The dyamic rage ceilig is M. Kivirata, H. Seppä, J. Pettilä, J. Hassel ad P. Helistö are with VTT the Techical Reasearch eter of Filad, Tietotie 3, Espoo, Filad. A.Virtae is with GE Healthcare Techologies, Nahkelatie 6, 43 Tuusula, Filad. TDM Pre distributed dyamic rage bottleecks FDM Oe flexible dyamic rage bottleeck Figure : The distributio of the dyamic rage budget i time domai ad frequecy domai multiplexers. usually determied by the SQUID oliearity. The dyamic rage floor is determied by the SQUID flux oise, whose value ca be multiplied by to take ito accout the cotributio of the back actio oise i the case where SQUIDs are oise matched to the cryogeic sesors. The flux oise Φ of dc SQUIDs (icludig SQUID arrays) is related to the SQUID power dissipatio P d by Φ P > k T. () d 6.8 B Φ For example, a SQUID with Φ = 7 Φ / Hz dissipates at least.94 W at mk. Because of the typical limit i the available coolig power, there is also a limit o the total dyamic rage budget of the readout system. This dyamic rage budged ca be distributed i differet ways: eg. there ca be a sigle SQUID with a large power dissipatio ad small Φ (ad cosequetly a large dyamic rage), or a umber of SQUIDs with smaller dissipatio ad a smaller dyamic rage. Note that there is a differece betwee TDM ad FDM i the way the dyamic rage budget is distributed betwee the pixels [3] (Fig. ). I the preferred TDM circuit topology the distributio is hard wired so that each pixel always gets a equal fractio of the total dyamic rage budget. This does ot matter i bolometer systems, where there is a sigal preset i all the pixels at all the time. otrary to this, i the preferred FDM circuit topology the sigals from a umber of pixels are summed before feedig them ito a sigle SQUID bottleeck. If o zero sigal is expected simultaeously from a few pixels oly, as is the case i photo coutig

2 calorimeters, the active pixel(s) ca temporarily use the total dyamic rage budget, icludig that of the eighborig idle pixels. Thus FDM has a advatage over TDM i calorimeter readouts. B. SQUID o liearity A voltage biased SQUID has more liear flux respose tha the same SQUID i curret biased cofiguratio (Fig. ). I order to get a crude estimate o the size of the effect, we have simulated umerically Josephso dyamics of a autoomous dc SQUID with β =.6 ad β L =, ad made a polyomial least squares fit to the flux respose at. Φ above the curve miimum. The simulatios were performed at bias poits close to the maximum modulatio depth. These choices reflect a typical (but liearity wise, probably o optimal) choice of the operatig poit i a real SQUID system. For the voltage bias the obtaied fit is I SQ = I + I ( φ.48φ +.45φ +.5φ 46φ ) whereas for the curret bias it is U SQ = U + U ( φ 3.3φ 9.φ φ φ ), where φ is the deviatio from the setpoit i the uits of flux quata. A similar fit to the characteristics of a real dc SQUID [4] with a voltage like bias from a.5 Ω source yields I SQ = I + I ( φ.65φ.φ + 5.5φ 4φ ). The SQUID liearity is a crucial bottleeck i desig of a FDM system [5]. Whe measurig the eergy of a registered photo, i.e. area of the curret pulse from the TES with a accuracy of 4, the quadratic o liearity limits the tolerable flux excursio below 4 4 Φ i the voltage biased case ad below 6 5 Φ i the curret biased case. Negative feedback, fortuately, liearizes the respose ot oly by reducig the flux excursio ad thus reducig the geeratio of the oliear sigal, but by additioally feedig back the (partial) correctio for the remaiig oliear sigal. This meas that a reasoable closed loop gai, possibly i cojuctio with post distortio of the sigal, leads to sufficiet liearizatio. The post SQUID amplifier stage is importat because it must ot degrade the SQUID oise, as this would decrease the available dyamic rage ad icrease the eed for the hard to obtai loop gai further.. Two stage SQUID amplifier Desig of a room temperature amplifier capable to udercut the output oise temperature of a SQUID at 4. K is a challegig task. The challege ca be alleviated by usig a secod cryogeic amplifier stage, which, however, must ot become the domiat dyamic rage bottleeck. Oe possibility is to use a SQUID series array [6], which is capable to deliver more sigal power to the room temperature amplifier tha a sigle SQUID. The importat desig k f = I M which parameter is the the flux ratio ( ) tells how may flux quata are iduced i each costituet I the FDM, however, the :th order correctio is at times the carrier frequecy, affectig the closed loop badwidth requiremet. SQUID of the array whe oe flux quatum is applied to the first SQUID. k f depeds o the curret gai I/ Φ of the st SQUID SQUID voltage (a) SQUID curret Applied flux [ Φ ] (b) Applied flux [ Φ ] Figure : Simulated flux respose of (a) curret biased ad (b) voltage biased dc SQUID. The visible ripple is the Josephso oscillatio remaiig after sigal averagig. Least squares fits to a 5 th order polyomial are depicted. ad mutual iductaces M of the SQUIDs formig the array. If oe chose k f.5, the secod order oliearities of the (typically) voltage biased st SQUID ad the curret biased array SQUID would cotribute equally to the total oliearity. Writig the oise temperature T at the output of a sigle SQUID ( = ) or a SQUID array ( > ) as V 4k BT = Φ /( Rd ) () Φ i terms of flux oise Φ ad voltage gai V/ Φ of each costituet SQUID suggests that the T does ot chage whe is icreased. If flux oise Φ of the st SQUID rather tha the self oise of the array domiates, oe ca write V BT = k f Φ ( Rd ) (3) 4k / Φ ad higher oise temperatures tha ~.4 T bath at the output become possible. Note, however, that oe would eed i the order of > / k f SQUIDs i series before the oise floor will be domiated by the st SQUID, which may be quite large a umber 3. Eve larger is required i practice because the power dissipatio typically forces oe to put the array at T = 4. K rather tha T = mk stage, which meas Φ > Φ. The above costrait is replaced by > T / (T k f ) i this case. Oe would coclude that a low T post SQUID amplifier is ecessary eve i the case of the two stage SQUID amplifier i order to avoid ridiculously large SQUID arrays. Ratio of the d order oliearity coefficiets i voltage ad curret biased cases. 3 Idetical SQUIDs assumed for the st SQUID ad for the costituet SQUIDs of the array.

3 3 III. ROOM TEMPERATURE SEMIONDUTOR DEVIES Bipolar trasistors such as MAT3 [7], SSM [8] or bipolar iput operatioal amplifiers AD797, LMH664 has FET type [publicatio] 5MHz R 5MHz Toshiba SK46/7 [] 9 K 69 Ω Iterfet IF3 [3] 3 K.6 kω Iterfet IF36 [4] 4 K 7 Ω Philips BF86. K 5. kω Table : Theoretical oise temperatures of some JFETs.used i post SQUID amplifiers. bee used ofte as the amplifyig elemets i post SQUID amplifiers. Their voltage oise is usually modelled [9] to be due to the base spreadig resistace R BB ad the shot oise due to collector curret I reactig o the base emitter juctio ( ) ( k BT ) u = 4 kbtrbb +. (4) ei ad the curret oise is the shot oise due to the base curret i = ei / h. (5) Whe eglectig R BB ad combiig the expressios ito T = T /, (6) h fe oe otices that extremely large values of curret gai h fe are eeded to reach T below ~ K. Usually the R BB related term domiates so that the T reachable i practice is eve worse. This applies to eg. Zetex FZT69 for which we have measured u ~ V Hz / implyig T = 36 K regardless of its high h fe = 4. The advatages of bipolar trasistors are (i) T does ot deped o frequecy, ad (ii) oise matchig resistace R h 6mV / I teds to be reasoably close to the opt fe source resistace of the SQUID. For JFETs the oise equatios from [9] at frequecy f ca be combied ito T = T f / (7) f where the oise badwidth f = g / π (8) m depeds o the FET fabricatio techology. The above oise temperature is reached for a resistive source oly whe the oise matchig coditio R =.6 / f (9) fe opt g is met. I commercialy available discrete silico JFETs the f ca approach GHz, whereas for GaAs ad IP MESFETs ad HEMTs f may be tes or hudreds of GHz. GaAs ad IP based devices have i the past bee cosidered useless i the low MHz frequecy rage because of their high /f oise, but there are some sub aovolt oise levels obtaied recetly [][] at cryogeic temperatures. The characteristic values for a few JFET types calculated at 5 MHz which have bee used i readouts of cryogeic circuits g are depicted i Table. Amog those, the BF86 is the most promisig type, because of its large ratio of trascoductace g m to iput capacitace g. The R opt values ted to be too high for SQUID readout. Impedace trasformatio is the ecessary, by (i) couplig Figure 3: Simplified schematic of the amplifier several FETs i parallel, (ii) usig a trasformer, or (iii) couplig several SQUIDs i series. IV. AMPLIFIER DESIGN We have costructed a amplifier card (Figs. 3 ad 4), also cotaiig the circuits eeded for SQUID bias ad test sigal feeds [5]. The first stage of our amplifier cosists of four FET cascodes coupled i parallel. The iput oise resistace level is further decreased by a :4 trasformer, woud o a Amido T37 6 toroidial core. Stray iductace of the trasformer has bee used to tue out the gate source capacitace of the FETs i the operatig frequecy rage. The cascode circuit reduces the badwidth limitig effect due to the gate drai (Miller) capacitace of the lower FET. The gate drai capacitace of the upper FET has bee tued out by a iductor i the drai. Each JFET is operated at ma drai curret. Active egative feedback has bee utilized to realize a effective 96 Ω resistive load at the cascode iput, which over the trasformer acts as a 6 Ω termiatio suitable for twisted pairs. The 3 db bad of the amplifier exteds from.8 MHz to 7.8 MHz. The omial voltage gai is 7 V/V. A simplified schematic is show i Fig. 3. There is a separate dc coupled sigal path cotaiig the SQUID bias circuitry ad a AD797 based low frequecy amplifier for moitorig the SQUID setpoit. V. MEASURED NOISE The oise performace of the amplifier was measured at 5 MHz usig Ω, 5 Ω, Ω, Ω ad 56 Ω resistors as iput termiatios at 94 K ad 77 K. The oise temperatures were the calculated usig the Y factor method. The 5 Ω figure was further checked with the source resistor at 4. K. The results are show i fig. 5. The data fits well to a model havig the iput referred voltage oise of u =. V Hz / ad curret oise of i = 3.5 pa Hz /. This would

4 4 traslate ito the optimal oise temperature of T = 7 K ad oise matchig resistace of R opt = 6 Ω. The reached oise temperature is above the theoretical value, for reasos which require further ivestigatio. I order Figure 4: Photograph of the amplifier prototype card. to rule out the cotributio of the trasformer core losses, the trasformer was tued with a capacitor ad a Q factor of 6 was measured. This traslates ito a ~ K cotributio to T. The modeled oise cotributio from the feedback resistor does ot explai the discrepacy, either. Some remaiig cadidates for the cause are (i) more complex system level iteractio betwee the amplifier stages, (ii) oise or rectified rf iterferece coupled from supply/bias lies, or (iii) the FETs ot reachig their theoretically estimated performace, eve approximately. A compariso with pre existig desigs such as [7] (T = 77 K), [8] (T = 89 K), [3] (T = 45 K, scaled from 6 MHz ito 5 MHz), or the AD797 op amp (T = 65 K) is a bit ufair because the above desigs are optimized for a differet applicatio ad with differet costraits, but it puts the the oise temperature achieved i this work to some sort of a perspective. Noise temperature (K) Source resistace (ohm) Figure 5: The measured oise temperature of the amplifier at f = 5 MHz with various source resistaces. A fit to the model u =. V/ Hz ad i = 3.5 pa/ Hz is depicted. Output sigal PSD (V / rthz) µφ / Hz / Frequecy (MHz) Figure 6: Noise spectrum at the amplifier output whe operated with a SQUID. The measured trasfer fuctio is 38 mv / Φ at 6 MHz. The amplifier was also coupled to a washer type SQUID [4] havig a o chip itegrated :5 output trasformer. The trasformer boosts the SQUID dyamic resistace R d. Ω ito 3 Ω level ad the SQUID gai V/ Φ µv/φ ito mv/φ level at frequecies above ~.5 MHz. A flux oise level of.45 µφ / Hz at 5 MHz was measured with the JFET electroics whe the SQUID was operated at 4. K. This is slightly more tha the.36 µφ / Hz oe would compute from the SQUID parameters ad the amplifier oise data above. The measured oise spectrum i fig. 4 suffers from iterferece origiatig from the spectrum aalyzer, which may explai the excess oise. VI. SIGE BIPOLAR TRANSISTORS We have experimeted with a umber of SiGe bipolar trasistors. Most otably, the Ifieo BFP65 has exhibited voltage oise below.3 V Hz / at room temperature ad below. V Hz / at 4. K (Fig. 7). The room temperature white voltage oise is cosistet with Johso oise from R BB =.5 Ω ad I c = 5 ma shot oise actig o the B E juctio (Eq. 4). At room temperature the SiGe based amplifier has the advatage of lower power cosumptio tha oe utilizig the BF86 JFETs. At cryogeic temperatures the reductio of the oise temperature is ot very large, but it is more importat that 4. K operatio (i) opes the possibility to use short egative feedback for icreasig the SQUID dyamic rage, ad (ii) avoids the oise cotributio due to Johso oise i the cryostat wirig. There are idicatios [6] that the power cosumptio of the SiGe devices could be reduced ito sub mw rage, which would facilitate multi chael operatio i closed cycle refrigerators. VII. ONLUSION The high frequecy oise performace of our amplifier compares favourably with pre existig desigs ad is

5 5 comparable to the recetly itroduced widebad electroics [7]. Its performace is likely to be exceeded, however, by applyig SiGe discrete bipolar trasistors which have become [6] Araboldi, Boella G ad Pessia G 3 IEEE Tras. Nucl. Sci [7] Drug D, these proceedigs. Noise [V / Hz / ] p k k M Frequecy [Hz] Figure 7: Noise spectrum of the BFP65 trasistor at 4. K with a 3.3 Ω resistor as the iput termiatio. The bias poit is Ic = 5 ma ad Vce =.5 V. The 4 MHz cutoff is due to the cable capacitace of the dipstick. available recetly. The JFET amplifier described i this paper remais still a useful buildig block for experimetig with frequecy domai multiplexed sesor arrays. VIII. AKNOWLEDGEMENT We thak Ja va der Kuur ad Piet de Korte for cotributios to the TDM vs FDM compariso ad o the effect of oliearities, which are worth a dedicated separate paper. Fiacial support from TEKES the Natioal Techology Agecy of Filad is gratefully ackowledged. REFERENES [] Kivirata M, va der Kuur J, Seppä H ad de Korte P A J 3 Proc. far IR, sub mm & mm detector techology workshop, NASA/P [] Irwi K. D. Physica [3] Va der Kuur J, Kivirata M ad de Korte P A J 3 Xeus IS WP 5 report, upublished. [4] Kivirata M, Pettilä J S, Gröberg L, Hassel J, Virtae A ad Seppä H 4, Supercod. Sci. Tech. 7 S85 9. [5] Va der Kuur J et al 5, th It'l Workshop o Low Temperature Detectors (LTD ), Tokyo, Japa. Submitted to Nucl. Istrum. Methods Phys. Res., Sect. A. [6] Welty R P ad Martiis J M 993 IEEE Tra. Appl. Supercod [7] Oukhasky N, Stolz R, Zakosareko V ad Meyer H G Physica [8] Drug D, Bechstei S, Frake K P, Scheier M ad Schurig Th IEEE Tras. Appl. Supercod [9] Buckigham M J 983 Noise i electroic devices ad systems (hichester: Ellis Horwood) [] Robiso A M ad Talyaskii V I 4 Rev. Sci. Istr [] Oukhaski N, Grajcar M, Il'ichev E ad Meyer H G 3 Rev. Sci. Istr [] Ryhäe T, Seppä H, Ilmoiemi R ad Kuutila J 989 J. Low Temp. Phys [3] Koch R H at al 996 Rev. Sci. Istrum [4] Helistö P, Sipola H, Pettilä J S, Seppä H, Kiue K, Nevala M ad Maasilta I, these proceedigs. [5] Virtae A 4, Masters thesis, Helsiki Uiversity of Techology (i fiish).